Theory of bifurcation amplifiers utilizing the nonlinear dynamical response of an optically damped mechanical oscillator

We consider a standard optomechanical system where a mechanical oscillator is coupled to a cavity mode through the radiation pressure interaction. The oscillator is coherently driven at its resonance frequency, whereas the cavity mode is driven below its resonance, providing optical damping of the mechanical oscillations. We study the nonlinear coherent response of the mechanical oscillator in this setup. For large mechanical amplitudes, we find that the system can display dynamical multistability if the optomechanical cooperativity exceeds a critical value. This analysis relates standard optomechanical damping to the dynamical attractors known from the theory of optomechanical self-sustained oscillations. We also investigate the effect of thermal and quantum noise and estimate the noise-induced switching rate between the stable states of the system. We then consider applications of this system and primarily focus on how it can be used as bifurcation amplifiers for the detection of small mechanical or optical signals. Finally, we show that in a related but more complicated setup featuring resonant optomechanical interactions, the same effects can be realized with a relaxed requirement on the size of the mechanical oscillations.Comment: 20 pages, 12 figure

Scheme for steady-state preparation of a harmonic oscillator in the first excited state

We present a generic quantum master equation whose dissipative dynamics autonomously stabilizes a harmonic oscillator in the n=1 Fock state. A multi-mode optomechanical system is analyzed and shown to be an example of a physical system obeying this model. We show that the optomechanical setup enables preparation of a mechanical oscillator in a nonclassical steady state, and that this state indeed approaches a single phonon Fock state in the ideal parameter regime. The generic model may be useful in other settings, such as cavity or circuit quantum electrodynamics or trapped ion physics.Comment: 4 pages, 3 figures + supplementary (7 pages, 2 figures) v2: Minor changes, added a few reference

Foreign Ownership and Market Entry

When a firm wishes to sell in a foreign market, it can do so either by exporting to that market or by investing in a local production unit. The latter mode of servicing a foreign market is referred to as a foreign direct investment (FDI). International production has increased rapidly during the last two decades, and particularly since the second half of the 1980s. This paper describes the facts, explains why firms choose FDI, and evaluates FDI in terms of impact on host economies. Particular emphasis is placed on firms’ choice between the two types of foreign investment; “greenfields”, which involves the establishment of a new production facility, and cross-border mergers and acquisitions, which involves taking over an existing production unit in a foreign market. The paper also contains a fairly extensive discussion of the consequences of economic integration on market entry.

Covariant representations for matrix-valued transfer operators

Motivated by the multivariate wavelet theory, and by the spectral theory of transfer operators, we construct an abstract affine structure and a multiresolution associated to a matrix-valued weight. We describe the one-to-one correspondence between the commutant of this structure and the fixed points of the transfer operator. We show how the covariant representation can be realized on $\mathbb{R}^n$ if the weight satisfies some low-pass condition.Comment: new version, motivation adde